AMHERST, New Hampshire Republican presidential hopeful Ron Paul declared on Wednesday his campaign was "peaking at the right time" as polls show him closing in on the two perceived front-runners.

The libertarian congressman from Texas with a passionate core of followers complained that pundits were dismissing his longshot campaign prematurely and sounded optimistic about catching former Massachusetts Governor Mitt Romney and former House of Representatives speaker Newt Gingrich.

All three and others are seeking to represent the Republicans and unseat Democratic President Barack Obama next November. The first of a series of Republican nominating contests is set for January 3 in Iowa.

"The momentum is building up and a lot of the candidates so far would come and go. They would shoot to the top and drop back rapidly. Ours has been very steady growth, then in this last week or two there has been a sudden extra growth," Paul told reporters after meeting voters in Amherst, New Hampshire.

Public Policy Polling released a survey on Tuesday showing him one percentage point behind Gingrich for the lead in Iowa.

Paul took 21 percent in the survey compared to 22 percent for Gingrich with Romney third at 16 percent.

In New Hampshire, which follows Iowa's caucus with a primary election on January 10, Romney led with 33 percent in a Rasmussen Reports poll released on Tuesday. Gingrich was second with 22 percent and Paul third at 18 percent. Paul's four-point gap behind Gingrich narrowed from a 10-point gap in the previous week's poll and marked Paul's best showing so far, Rasmussen said.

"In political terms, it probably means we're peaking at the right time," Paul said.

INFLUENCE THE RACE

Paul, who is making his third bid for the White House, is unlikely to take the nomination. But he may influence the race all the way to the end, acquiring delegates that stand to give him clout at the party's nominating convention next August.

He could tilt the nomination to one candidate should the race remain undecided by convention time.

"The other candidates are scared of him and his ability to attract strong supporters," said Jennifer Donahue, a fellow at the Eisenhower Institute at Gettysburg College.

"If Romney had a core like Paul does, no matter how small, he'd be much better off," Donahue said, referring to Romney's status as the establishment candidate.

Paul, 76, attracts voters with a libertarian vision of eliminating a role for the state wherever possible. But some of his views alienate traditional bases of the Republican Party.

His call to abolish the Federal Reserve alarms Wall Street Republicans. His advocacy for withdrawing from U.S. military engagements abroad concerns national security Republicans. Social conservatives may be wary of his refusal to oppose gay marriage, as Paul says the federal government has no business regulating any marriage.

"The special interests on Wall Street -- they might have a lot of money but they don't have a lot of voters," Paul said.

Loyal and boisterous followers flock to his campaign events, such as a town hall meeting in Peterborough, New Hampshire, on Tuesday.

"He doesn't think he's better than any of us. You can tell by the way he speaks to us. He seems very genuine and plain. He doesn't embellish," said Susan Davidson, 49.

"He's an extremely brave man to be able to speak his mind so simply but eloquently in the face of all the big stars and heroes in Congress. He's not afraid of them," she said.

Paul has also gained attention for television ads that have attacked Gingrich.

"He definitely takes more from Gingrich than he does from Romney," said Ford O'Connell, a Republican strategist who said he is neutral in the nominating process. "He's doing to Newt Gingrich what Romney hasn't been able to do. In a lot of ways he's Newt Gingrich's worst nightmare."

(Editing by Xavier Briand)

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